Theresa May: ‘The 27 will sign up to a deal with us.’
Photograph: Andy Rain/EPA

Theresa May has dismissed threats by EU countries to veto Brexit negotiations with the UK, as she declared: “The 27 will sign up to a deal with us.”

The prime minister said other nations would accept an agreement with Britain after the Slovakian prime minister said that four central European countries were willing to block talks unless their citizens retained their rights to work in the UK. Robert Fico said last week that Slovakia, Poland, the Czech Republic and Hungary would be “uncompromising” during talks and ready to veto arrangements “unless we feel a guarantee that these people are equal”.

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However, May rejected such warnings when asked whether it would really be possible to secure the agreement of all other member states for Brexit and trade talks. “The 27 will sign up to a deal with us,” she said. “We will be negotiating with them. And … we will be ambitious in what we want to see for the UK. A good deal for the UK can also be a good deal for the other member states because I believe in good trading relations and I have said I want the UK to be a global leader in free trade.”

Stressing that the other EU countries would have something to gain from a deal being struck, May added: “This is not just about us, it’s actually about their relationships and trading within that European arena.”

May’s position is more optimistic than that of David Davis, the Brexit secretary, who last week said there was a possibility the UK could leave the EU without a deal and would have to fall back on default World Trade Organisation tariffs.

Although the main Brexit negotiations are separate from trade talks, EU countries have made it clear that the UK will have to sign up to some degree of free movement if it wants access to the single market. May has said there must be controls on free movement as a priority in negotiations, but left the door open for EU citizens to be able to work and travel in the UK on preferential terms. This would disappoint those in her party pushing for a “hard Brexit” who want to leave the single market completely and end the free movement of EU citizens to the UK.

May made the comments as she flew to New York for the UN general assembly, where she is embarking on a charm offensive with US businesses such as Goldman Sachs, Amazon, Morgan Stanley, IBM and Black Rock in an effort to calm concerns over Brexit. As well as reassuring them about the state of the economy, she will need to convince those that use the UK as a European headquarters that there will still be strong tariff-free trading with EU countries.

Countries such as Japan have already warned the UK that a lack of clarity about Brexit and loss of the benefits that access to the single market brings could lead some of its investors to move away. May will have her second meeting in a fortnight with Shinzo Abe, the Japanese prime minister, at the UN summit, after Tokyo delivered the warning at the G20 in Hangzhou earlier in the month.

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The prime minister is hosting a party on Monday night for US and British investors to reassure them that relations will continue between the two countries after Brexit.

“What I will be talking about with both American and British leaders is about how we can encourage that trade and investment between the countries. Something like a million people wake up each morning and go to work for an American company,” May said, ahead of the summit.

May is being accompanied on the trip by Boris Johnson, the foreign secretary, and Priti Patel, the international development secretary, but not Liam Fox, the trade secretary, who painted UK companies as too “fat and lazy” to be interested in exporting.

Asked about the comments, the prime minister appeared to defend her senior cabinet minister. “We all put things in different ways,” she said. “What Liam is doing is encouraging businesses to export, which is an important part of his role as trade secretary.”